• An ID card does not guarantee that the bearer has not subsequently been deemed mentally incompetent nor convicted of a crime that disqualifies them from firearms ownership.
• Your proposal would require anyone who has ever sold a gun to maintain records of the transfer indefinitely. In order to have teeth, you'd have to create a new crime for failure to do so. Even federally licensed firearms dealers don't have to maintain records indefinitely.
All this aside, there is the larger issue that the kinds of events that prompt such proposals (Sandy Hook, Santa Barbara, San Bernardino, Charleston) have perpetuators who either passed NCIC or would have if they went through a dealer. And while mass shootings are what get all the news coverage, they are hardly representative of the average shooting, where the guns tend to have been acquired illegally already.